#include "paint.h"
#include <bits/stdc++.h>
using namespace std;
const int N = 5000 + 2;
bitset<N> targB, targW;
array<vector<bitset<N>>, 2> dpB, dpW;
array<vector<bool>, 2> valid;
string solve_puzzle(string s, vector<int> c) {
int k = c.size(), n = s.size();
if(n > N)return "";
for(int i = 0; i < n; i++)targB[i+2] = s[i] == 'X', targW[i+2] = s[i] == '_';
for(auto& i: dpB)i.resize(n+2);
for(auto& i: dpW)i.resize(n+2);
for(auto& i: valid)i.resize(n+2);
auto stringify = [n](int x, int y){
string ans = "";
if(!valid[x][y])return (string)"INVALID";
for(int i = 2; i < n+2; i++){
//assert(dpW[n][k][i] || dpB[n][k][i]);
if(dpW[x][y][i] && dpB[x][y][i]) ans += '?';
else if(dpW[x][y][i]) ans += '_';
else if(dpB[x][y][i]) ans += 'X';
else ans += '!';
}
return ans;
};
valid[0][0] = 1;
for(int i = 1; i <= n+1; i++){
valid[0][i] = 1, dpW[0][i] = dpW[0][i-1];
dpW[0][i][i] = 1;
}
//cout << "hi" << endl;
for(int j = 1; j <= k; j++){
for(int i = 0; i < n+2; i++)dpW[j&1][i].reset(), dpW[j&1][i].reset(), valid[j&1][i] = 0;
for(int i = 2; i < n+2; i++){
if(i <= c[j-1] || !valid[!(j&1)][i-c[j-1]-1]){
if(valid[j&1][i-1] && !targB[i]) dpW[j&1][i] = dpW[j&1][i-1], dpB[j&1][i] = dpB[j&1][i-1], dpW[j&1][i][i] = 1, valid[j&1][i] = 1;
continue;
}
valid[j&1][i] = 1;
dpW[j&1][i] = dpW[!(j&1)][i-c[j-1]-1];
dpB[j&1][i] = dpB[!(j&1)][i-c[j-1]-1];
//if(i != c[j-1])
dpW[j&1][i][i-c[j-1]] = 1;
for(int x = i-c[j-1]+1; x <= i; x++)dpB[j&1][i][x] = 1;
//cout << i-1 << " " << j << " " << stringify(i, j) << endl;
if(((dpB[j&1][i] & targW) | (dpW[j&1][i] & targB)).count())
dpW[j&1][i] = dpW[j&1][i-1], dpB[j&1][i] = dpB[j&1][i-1], valid[j&1][i] = valid[j&1][i-1], dpW[j&1][i][i] = 1;
else if(valid[j&1][i-1] && !targB[i]) dpW[j&1][i] |= dpW[j&1][i-1], dpB[j&1][i] |= dpB[j&1][i-1], dpW[j&1][i][i] = 1;
if(dpW[j&1][i][i] && targB[i])valid[j&1][i] = 0, dpW[j&1][i][i] = 0;
//cout << i-1 << " " << j << " " << stringify(i, j) << endl;
}
}
return stringify(k&1, n+1);
}
